Iteration

The classes of the Iteration cluster encapsulate control structures representing common traversal operations.

Iterators and Agents

The recent introduction of the agents mechanism in ISE Eiffel offers an attractive alternative to the Iterator cluster of EiffelBase.

The Notion of iterator

Let us first explore the role of iterators in the architecture of a system.

Iterating over data structures

Client software that uses data structures of a certain type, for example lists or trees, often needs to traverse a data structure of that type in a predetermined order so as to apply a certain action to all the items of the structure, or to all items that satisfy a certain criterion. Such a systematic traversal is called an iteration.
Cases of iteration can be found in almost any system. Here are a few typical examples:

A text processing system may maintain a list of paragraphs. In response to a user command, such as a request to resize the column width, the system will iterate over the entire list so as to update all paragraphs.
A business system may maintain a list of customers. If the company decides that a special promotion will target all customers satisfying a certain criterion (for example all customers that have bought at least one product over the past six months), the system will iterate over the list, generating a mailing for every list item that satisfies the criterion.
An interactive development environment for a programming language may maintain a syntax tree. In response to a program change, the system will traverse the tree to determine what nodes are affected by the change and update them.

These examples illustrate the general properties of iteration. An iteration involves a data structure of a known general type and a particular ordering of the structure’s items. For some structures, more than one ordering will be available; for example a tree iteration may use preorder, postorder or breadth-first (as defined below). The iteration involves an operation, say item_action, to be applied to the selected items. It may also involve a boolean-valued query, say item_test, applicable to candidate items. Finally, it involves a certain policy, usually based on item_test, as to which items should be subjected to item_action. Typical example policies are:

Apply item_action to all the items in the structure. (In this case item_test is not relevant).
Apply item_action to all items that satisfy item_test.
Apply item_action to all items up to the first one that satisfies item_test.

The Iteration library provides many more, covering in particular all the standard control structures.

Iterations and control structures

You can perform iterations without any special iteration classes. For example if customers is declared as

customers: LIST [CUSTOMER]

then a class SPECIAL_PROMOTION of a text processing system may include in one of its routines a loop of the form

from
    customers.start
until
    customers.exhausted
loop
    if recent_ purchases.has (customers.item) then
        target_list.put (customers.item)
    end
    customers.forth
end

Such schemes are quite common. But it is precisely because they occur frequently that it is useful to rely on library classes to handle them. One of the principal tasks of object-oriented software development is to identify recurring patterns and build reusable classes that encapsulate them, so that future developers will be able to rely on ready-made solutions.
The classes of the Iteration library address this need. Using them offers two benefits:

You avoid writing loops, in which the definition of sub-components such as exit conditions, variants and invariants is often delicate or error-prone.
You can more easily adapt the resulting features in descendant classes. The rest of this chapter shows how to obtain these benefits.

Simple Examples

To get a first grasp of how one can work with the Iteration library, let us look at a typical iteration class and a typical iteration client.

An example iterator routine

Here, given with its full implementation, is a typical Iteration library routine: the procedure until_do from LINEAR_ITERATOR, the class defining iteration mechanisms on linear (sequential) structures.

until_do is
        -- Apply action to every item of target,
        -- up to but excluding first one satisfying test.
        -- (Apply to full list if no item satisfies test.)
    require
        traversable_exists: target /= Void
    do
        from
            target.start
        invariant
            invariant_value
        until
            target.exhausted or else test
        loop
            action
            target.forth
        end
    ensure
        achieved: target.exhausted or else test
        invariant_satisfied: invariant_value
    end

The precise form of the procedure in the class relies on a call to another procedure, until_continue, and on inherited assertions. Here everything has been unfolded for illustration purposes.
This procedure will traverse the linear structure identified by target and apply the procedure called action on every item up to but excluding the first one satisfying test.
The class similarly offers do_all, do_while, do_for, do_if and other procedures representing the common control structures. It also includes functions such as exists and forall, corresponding to the usual quantifiers.
These iteration schemes depend on the procedure action, defining the action to be applied to successive elements, and on the function test, defining the boolean query to be applied to these elements. These features are declared in class ITERATOR (the highest-level deferred class of the Iteration library); here is test:

test: BOOLEAN is
        -- Test to be applied to item at current position in
        -- target (default: value of item_test on item)
    require
        traversable_exists: target /= Void
        not_off: not target.off
    do
        Result := item_test (target.item)
    ensure
        not_off: not target.off
    end

This indicates that the value of the boolean function test will be obtained by applying item_test to the item at the current position in the target structure. In ITERATOR, function item_test always return False; descendant classes will redefine it so as to describe the desired test. Similarly, action is declared in class ITERATOR as a call to item_action. Descendants will redefine item_action, which as initially declared in ITERATOR is a procedure with a null body.
Going through item_action and item_test provides an extra degree of flexibility. Normally the action and test performed at each step apply to target.itemitem, so that it suffices to redefine the item_features. This is the case will all examples studied in this chapter. In a more general setting, however, you might need to redefine action and test themselves.

An example use of iteration

Here now is an example illustrating the use of these mechanisms. The result will enable us to resize all the paragraphs of a text up to the first one that has been modified - as we might need to do, in a text processing system, to process an interactive user request. Assume a class TEXT that describes lists of paragraphs with certain additional features. The example will also assume a class PARAGRAPH with a procedure resize, and a boolean-valued attribute modified which indicates whether a paragraph has been modified. Class TEXT inherits from LINKED_LIST and so is a descendant of LINEAR:

class
    TEXT

inherit
    LINKED_LIST [PARAGRAPH]
    ...

feature
    ...

end

In a class TEXT_PROCESSOR, you can use an iteration procedure to write a very simple procedure resize_ paragraphs that will resize all paragraphs up to but excluding the first one that has been modified:

class
    TEXT_PROCESSOR

inherit
    LINEAR_ITERATOR [PARAGRAPH]
        redefine
            item_action, item_test
        end

feature

    resize_ paragraphs (t: TEXT) is
        -- Resize all the paragraphs of t up to but excluding         -- the first one that has been modified.
    do
        set (t)
        until_do
    end

feature {NONE}

    item_test (p PARAGRAPH): BOOLEAN is
        -- Has p been modified?
    do
        Result := p.modified
    end

    item_action (p: PARAGRAPH) is
        -- Resize p.
    do
        p.resize
    end

    ...
end

Thanks to the iteration mechanism, the procedure resize_ paragraphs simply needs two procedure calls:

To set its argument t as the iteration target, it uses procedure set. (This procedure is from class ITERATOR which passes it on to all iterator classes.)
Then it simply calls until_do as defined above.

Procedure item_action is redefined to describe the operation to be performed on each successive element. Function item_test is redefined to describe the exit test.
As presented so far, the mechanism seems to limit every descendant of an iteration class to just one form of iteration. As shown later in this chapter, it is in fact easy to generalize the technique to allow a class to use an arbitrary number of iteration schemes.
What is interesting here is that the redefinitions of item_test and item_action take care of all the details. There is no need to write any loop or other control structure. We are at the very heart of the object-oriented method, enjoying the ability to encapsulate useful and common software schemes so that client developers will only need to fill in what is specific to their application.

Using the Iteration Library

Let us now explore the classes of the Iteration library and the different ways of using them.

Overview of the classes

There are only four Iteration classes, whose simple inheritance structure appeared at the beginning of this chapter.

ITERATOR, a deferred class which describes the most general notion.
LINEAR_ITERATOR, for iterating over linear structures and chains.
TWO_WAY_CHAIN_ITERATOR, a repeated heir of LINEAR_ITERATOR, for iterating in either direction over a bilinear structure.
CURSOR_TREE_ITERATOR, for iterating over trees.

As you will remember from the presentation of the abstract overall taxonomy, the traversal hierarchy describes how data structures can be traversed; its most general class is TRAVERSABLE.
Each one of the iterator classes is paired with a traversal class (or two in one case):

ITERATOR	TRAVERSABLE
LINEAR_ITERATOR	LINEAR
TWO_WAY_CHAIN_ITERATOR	TWO_WAY_LIST
TWO_WAY_CHAIN_ITERATOR	TWO_WAY_LIST, TWO_WAY_CIRCULAR
CURSOR_TREE_ITERATOR	CURSOR_TREE

Each iterator class relies on the corresponding traversal class to provide the features for traversing the corresponding data structures, such as start, forth and exhausted for linear structures.
Of course the data structure class used in connection with a given iterator class does not need to be the iterator’s exact correspondent as given by the above table; it may be any one of its descendants. For example you may use LINEAR_ITERATOR to iterate over data structures described not just by LINEAR but also by such descendants as LIST, LINKED_LIST, ARRAYED_LIST, or even TWO_WAY_LIST if you do not need the backward iteration features (for which you will have to use TWO_WAY_CHAIN_ITERATOR ).

General iteration facilities

Class ITERATOR defines the features that apply to all forms of iterator.
An iterator will always apply to a certain target structure. The target is introduced in ITERATOR by the feature target: TRAVERSABLE [G]
Both the iterator classes and the traversal classes are generic, with a formal generic parameter G. The actual generic parameters will be matched through the choice of iteration target: for a generic derivation of the form SOME_ITERATOR [ACTUAL_TYPE] the target can only be of type SOME_TRAVERSABLE [ACTUAL_TYPE] for the same ACTUAL_TYPE, where SOME_TRAVERSABLE is the traversal class matching SOME_ITERATOR according to the preceding table (LINEAR for LINEAR_ITERATOR and so on), or one of its proper descendants.
Each of the proper descendants of ITERATOR redefines the type of target to the matching proper descendant of TRAVERSABLE, to cover more specific variants of the iteration target, For example in LINEAR_ITERATOR the feature is redefined to be of type LINEAR. ITERATOR also introduces the procedure for selecting a target:

set (s: like target) is
        -- Make s the new target of iterations.
    require
        s /= Void
    do
        target := s
    ensure
        target = s
        target /= Void
    end

Next ITERATOR introduces the routines describing the elementary action and test that will be applied to items of the iteration targets:

action is
        -- Action to be applied to item at current position in
        -- target.
        -- (default: item_action on item at current position.)
        -- Note: for iterators to work properly, redefined
        -- versions of this feature should not change the
        -- traversable structure.
    require
        traversable_exists: target /= Void
        not_off: not target.off
        invariant_satisfied: invariant_value
    do
        item_action (target.item)
    ensure
        not_off: not target.off
        invariant_satisfied: invariant_value
    end

These routines rely on two others, item_action and item_test, which both take an argument of type G, the formal generic parameter. The reason, already noted above, is that in a vast majority of cases the iterated action and test solely depend, at each step of the traversal, on the item (of type G) at the current position. To define an iteration process, then, it suffices to redefine item_action and item_test in a descendant of the appropriate iteration class. Only in complex cases will it be necessary to redefine action and test themselves.
If you encounter such a case, note the caveat about action changing the target’s structure. Understandably enough, an iterator that attempts to change the data structure while traversing it may engage in strange behavior. No such risk exists if you only redefine item_action, which may change the contents of items but not the structure itself.
Another feature introduced in ITERATOR is the query invariant_value, describing invariant properties that must be ensured at the beginning of any iteration and preserved by every iteration step. As declared in ITERATOR this query always returns true, but proper descendants can redefine it to describe more interesting invariant properties.
Finally, ITERATOR introduces in deferred form the general iteration routines applicable to all iteration variants. They include two queries corresponding to the quantifiers of first-order predicate calculus:

for_all will return true if all items of the target structure satisfy test.
exists will return true if at least one item satisfies test.

The other routines are commands which will traverse the target structure and apply action to items selected through test:

do_all applies action to all items.
do_if, to those items which satisfy test.
until_do, to all items up to but excluding the first one that satisfies test.
do_until, to all items up to and including the first one that satisfies test.
while_do and do_while, to all items up to the first one that does not satisfy test. (This can also be achieved with until_do or do_until by choosing the opposite test.)

All these features, and most of the other iteration features introduced in proper descendants of ITERATOR and described next, have no argument. Information about the target of iteration comes from feature target, set by procedure set; information about what needs to be done for each item of the target structure comes from item_action and item_test.

Linear and chain iteration

LINEAR_ITERATOR, an effective class, refines the iteration mechanisms for cases in which the target is a linear structure, such as a list in any implementation or a circular chain.
The class effects all the deferred features inherited from ITERATOR, taking advantage of the linear traversal mechanisms present in the corresponding traversal class, LINEAR. Here for example is the effecting of do_if:

do_if is
        -- Apply action to every item of target satisfying         -- test.
    do
        from
            target.start
        invariant
            invariant_value
        until
            target.exhausted
        loop
            if test then
                action
            end
            forth
        end
    end

This routine text relies on features start, forth and exhausted which, together with off, have for convenience been carried over to LINEAR_ITERATOR from their counterparts in LINEAR, with feature declarations such as

off: BOOLEAN is
        -- Is position of target off?
    require
        traversable_exists: target /= Void
    do
        Result := target.off
    end

and similarly for the others.
In addition to effecting the general iteration features from ITERATOR, class LINEAR_ITERATOR introduces iteration features that apply to the specific case of linear structures:

search (b: BOOLEAN) moves the iteration to the first position satisfying test if b is true, or not satisfying test if b is false. This use of a boolean argument to switch between two opposite semantics is not part of the recommended style, and you will find few if any other examples in the Base libraries. Here, however, it was deemed preferable to the alternative, which would have involved four separate procedures (if together with search we consider continue_search discussed next).
With a linear structure we can implement an iteration corresponding to the “for” loop of traditional programming languages, defined by three integers: the starting position, the number of items to be traversed, and the step between consecutive items. This is provided by procedure do_for (starting, number, step: INTEGER).
Since with a linear target the iterator can advance the cursor step by step, the basic iteration operations are complemented by variants which pick up from the position reached by the last call: continue_until, until_continue, continue_while, while_continue, continue_search, continue_for.

Two-way iteration

Class TWO_WAY_CHAIN_ITERATOR has all the features of LINEAR_ITERATOR, to which it adds features for iterating backward as well as forward.
The class introduces commands finish and back, applying the corresponding operations to the two-way target. It also has a backward variant for every iteration feature. The name of each such variant is the name of the forward feature followed by _back: do_all_back, until_do_back and so on.
An alternative design would have kept just one set of features and added two features: a command reverse to reverse the direction of future iteration operations, and a query backward to find out the direction currently in force.
Contrary to what one might at first imagine, class TWO_WAY_CHAIN_ITERATOR is extremely short and simple; its Feature clause only contains the declarations of two features, finish and back.
The trick is to use repeated inheritance. TWO_WAY_CHAIN_ITERATOR inherits twice from LINEAR_ITERATOR; the first inheritance branch yields the forward iteration features, the second yields those for backward iteration. There is no need for any explicit declaration or redeclaration of iteration features. Here is the entire class text that yields this result:

class
    TWO_WAY_CHAIN_ITERATOR [G]

inherit
    LINEAR_ITERATOR [G]
        redefine
            target
        select
            start,
            forth,
            do_all,
            until_do,
            do_until,
            do_if,
            do_for,
            search,
            forall,
            exists,
            until_continue,
            continue_until,
            continue_for,
            continue_search
        end

    LINEAR_ITERATOR [G]
        rename
            start as finish,
            forth as back,
            do_all as do_all_back,
            until_do as until_do_back,
            do_until as do_until_back,
            do_if as do_if_back,
            do_for as do_ for_back,
            search as search_back,
            forall as forall_back,
            exists as exists_back,
            until_continue as until_continue_back,
            continue_until as continue_until_back,
            continue_for as continue_for_back,
            continue_search as continue_search_back
        redefine
            target
        end

feature -- Status report

    target: BILINEAR [G]
            -- The structure to which iteration features will
            -- apply

feature -- Cursor movement

    finish is
            -- Move cursor of target to last position.
        do
            target.finish
        end

    back is
            -- Move cursor of target backward one position.
        do
            target.back
        end
end

This class provides a good example of the economy of expression that the full inheritance mechanism affords through the combination of renaming, redefinition, repeated inheritance rules and selection, without sacrificing clarity and maintainability.

Tree iteration

Tree iterations, provided by class CURSOR_TREE_ITERATOR, work on trees of the cursor tree form; only with this form of tree are traversal operations possible. Three forms of iteration are provided: preorder, postorder and breadth-first. They correspond to the three traversal policies described in the discussion of trees. Here too it would seem that a rather lengthy class is needed, but repeated inheritance works wonders.
CURSOR_TREE_ITERATOR simply inherits three times from LINEAR_ITERATOR, renaming the features appropriately in each case:

pre_do_all, pre_until and so on.
post_do_all, post_until and so on.
breadth_do_all, breadth_until and so on.

All it needs to do then is to redefine the type of target to be CURSOR_TREE [G], and to redefine six features: the three renamed start (pre_start etc.) and the three forth (pre_ forth and so on). These seven redefinitions give us a full-fledged battery of tree iteration mechanisms.

Building and Using Iterators

To conclude this discussion, let us now put together the various mechanisms studied so far, to see how authors of client software can use the Iteration library to perform possibly complex iterations on various data structures without ever writing a single loop or test. The basic ideas were sketched above but now we have all the elements for the full view.
An application class may use one of the iteration classes in either of two ways: as a descendant (single or repeated) or as a client. The descendant technique is extremely simple but less versatile.

The single descendant technique

Assume an application class PROCESSOR that is a proper descendant of one of the effective iteration classes studied in this chapter. Then a routine of PROCESSOR, say iterate, may iterate a certain action over a data structure, subject to a certain test. First, class PROCESSOR must specify the action by redefining item_action and item_test (or, in the most general case, action and test). Then routine iterate must specify the target data structure through a call of the form set (t) where t represents the selected target data structure. The type of t must correspond to the iteration class selected as ancestor of PROCESSOR: for LINEAR_ITERATOR it must be a descendant of LINEAR (such as LINKED_LIST, ARRAYED_LIST, LINKED_CIRCULAR or any other list or circular chain classes); for TWO_WAY_CHAIN_ITERATOR it must be a descendant of BILINEAR such as TWO_WAY_LIST or TWO_WAY_CIRCULAR; for CURSOR_TREE_ITERATOR it must be a descendant of CURSOR_TREE. In all cases the actual generic parameters of the iterator class and of the data structure class must be compatible. Then the iteration proper is obtained simply by calling the appropriate procedure, without any qualification or arguments, for example: do_ if
It is hard to imagine a simpler scheme: no loops, no initialization, no arguments. Feature item_action may need to rely on some variable values. Because it does not take any argument, such values will have to be treated as attributes, with the corresponding set_... procedures to set and change their values. This also applies to the two schemes set next.
The single descendant technique has one drawback: it provides the iterating class, PROCESSOR, with only one set of iteration particulars. This limitation does not affect the number of targets: you may use as many targets as you wish, as long as they are of compatible types, by calling a routine such as iterate several times, or calling several such routines, each call being preceded by a call to set to define a new target. The limitation also does not affect the iterating scheme: one iteration could use do_if, the next do_all and so on. But it does require the action and test to be the same in all cases.
The next two techniques will remove this limitation.

Using repeated inheritance

One way to obtain several iteration schemes is a simple extension to the single descendant technique. You can use repeated inheritance to provide two or more variants. We have in fact already encountered the technique when studying how to derive TWO_WAY_CHAIN_ITERATOR and CURSOR_TREE_ITERATOR from LINEAR_ITERATOR. The general pattern, applied here to just two iteration schemes but easily generalized to more, is straightforward:

class
    DUAL_PROCESSOR

inherit
    LINEAR_ITERATOR [SOME_TYPE]
        rename
            item_action as action1,
            item_test as test1,
            do_if as do_if1,
        redefine
            action1, test1
        select
            action1, test1
        end

    LINEAR_ITERATOR [SOME_TYPE]
        rename
            item_action as action2,
            item_test as test2,
            do_if as do_if2,
        redefine
            action2, test2
        end

feature

    action1 is
            -- Action for the first scheme
        do
            ...
        end

    test1: BOOLEAN is
            -- Test for the first scheme
        do
            ...
        end

    action2 is
            -- Action for the second scheme
        do
            ...
        end

    test2: BOOLEAN is
            -- Test for the second scheme
        do
            ...
        end

    iterate1 is
            -- Execute iteration of first kind.
        do
            set (...)
            do_if1
        end

    iterate2 is
            -- Execute iteration of second kind.
        do
            set (...)
            do_if2
        end

    ...

The repeated inheritance machinery takes care of the rest.

Using explicit iterator objects

To obtain maximum flexibility, classes that need iteration facilities should be clients rather than descendants of the iteration classes. The resulting scheme is completely dynamic: to perform iterations you use iterator objects as discussed earlier.
The following example illustrates the technique. Consider a deferred class FIGURE describing the notion of graphical figure, with many effective descendants (POLYGON, CIRCLE and so on). It is useful to define COMPLEX_FIGURE, describing figures that are recursively composed of sub-figures. This is a remarkable example of multiple inheritance:

class
    COMPLEX_FIGURE

inherit
    FIGURE,
    LINKED_LIST [FIGURE]

feature
    ... end

In the feature clause we want to provide the appropriate effectings for the deferred features of class FIGURE: display, hide, translate and all other basic figure operations.
We can use loops for that purpose, for example

display is
        -- Recursively display all components of the complex
        -- figure
    do
        from
            start
        until
            exhausted
        loop
            item.display
            forth
        end
    end

Although acceptable and even elegant, this scheme will cause significant duplication: all the FIGURE features - not just display but also hide, rotate, move and others - will have the same structure, with a loop. We can use iterators to avoid this duplication. The repeated inheritance technique would work, but given the large number of FIGURE features the amount of repeated inheritance that would be needed seems unwieldy. It is also not very desirable to have to change the inheritance structure of the system just to add a new feature to FIGURE. The more dynamic approach using iterator objects seems preferable.
To implement this approach, define a class for iterating on complex figures:

class
    COMPLEX_FIGURE_ITERATOR

inherit
    LINEAR_ITERATOR
        redefine
            target
        end

create
    set

feature
    target: COMPLEX_FIGURE

end

Then for each operation to be iterated define a small class. For example:

class
    FIGURE_DISPLAYER

inherit
    COMPLEX_FIGURE_ITERATOR
        redefine
            item_action
        end

create
    set

feature

    item_action (f: FIGURE) is
            -- Action to be applied to each figure: display
            -- it.
        do
            f.display
        end
    end

Similarly, you may define FIGURE_HIDER, FIGURE_MOVER and others. Then the features of COMPLEX_FIGURE are written almost trivially, without any explicit loops; for example:

display is
        -- Recursively display all components of the complex
        -- figure
    local
        disp: FIGURE_DISPLAYER
    do
        create disp.set (Current)
        disp.do_all
    end

and similarly for all the others.
Note the use of set as creation procedure, which is more convenient than requiring the clients first to create an iterator object and then to call set. This is also safer, since with set as a creation procedure the client cannot forget to initialize the target. (If a class C has a creation clause, the creation instruction create x with no creation call is invalid for x of type C.)